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Distinguish between the forces experienced by a moving charge in a uniform electric field and in a uniform magnetic field.

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A charge q moving with a velocity v through a magnetic field of induction B experiences a magnetic force perpendicular both to B and v . Experimental observations show that the magnitude of the force is proportional to the magnitude of B, the speed of the particle, the charge q and the sine of the angle θ between v and B. That is, the magnetic force, Fm = qv B sin θ
Fm=q(v×B)
Therefore, at every instant Fm acts in a direction perpendicular to the plane of v and B .

If the moving charge is negative, the direction of the force Fm acting on it is opposite to that given by the right-handed screw rule for the cross-product v × B.

If the charged particle moves through a region of space where both electric and magnetic fields are present, both fields exert forces on the particle.
The force due to the electric field E is Fe=qE .
The total force on a moving charge in electric and magnetic fields is called the Lorentz force :
F=Fe+Fm=q(E+v×B)
Special cases :
(i) v is parallel or antiparallel to B: In this case, Fm = qvB sin 0° = 0. That is, the magnetic force on the charge is zero.
(ii) The charge is stationary {v = 0) : In this case, even if q ≠ 0 and B ≠ 0, Fm = q(0)B sin θ = 0. That is, the magnetic force on a stationary charge is zero.

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